[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------[/tex]
[tex]\bf \textit{"volume of a gas varies inversely with the pressure"}\quad v=\cfrac{k}{p}
\\\\\\
\textit{we also know that }
\begin{cases}
v=7\\
p=410
\end{cases}\implies 7=\cfrac{k}{210}\implies 1470=k
\\\\\\
thus\qquad \qquad \boxed{v=\cfrac{1470}{p}}
\\\\\\
\textit{when p=287, what is \underline{v}?}\qquad v=\cfrac{410}{287}[/tex]
